Abstract
Determinations of the proton's collinear parton distribution functions (PDFs) are emerging with growing precision due to increased experimental activity at facilities like the Large Hadron Collider. While this copious information is valuable, the speed at which it is released makes it difficult to quickly assess its impact on the PDFs, short of performing computationally expensive global fits. As an alternative, we explore new methods for quantifying the potential impact of experimental data on the extraction of proton PDFs. Our approach relies crucially on the Hessian correlation between theory-data residuals and the PDFs themselves, as well as on a newly defined quantity --- the sensitivity --- which represents an extension of the correlation and reflects both PDF-driven and experimental uncertainties. This approach is realized in a new, publicly available analysis package PDFSense, which operates with these statistical measures to identify particularly sensitive experiments, weigh their relative or potential impact on PDFs, and visualize their detailed distributions in a space of the parton momentum fraction $x$ and factorization scale $\mu$. This tool offers a new means of understanding the influence of individual measurements in existing fits, as well as a predictive device for directing future fits toward the highest impact data and assumptions. Along the way, many new physics insights can be gained or reinforced. As one of many examples, PDFSense is employed to rank the projected impact of new LHC measurements in jet, vector boson, and $t\bar{t}$ production and leads us to the conclusion that inclusive jet production at the LHC has a potential for playing an indispensable role in future PDF fits. These conclusions are independently verified by preliminarily fitting this experimental information and investigating the constraints they supply using the Lagrange multiplier technique.
Highlights
The determination of collinear parton distribution functions (PDFs) of the nucleon is becoming an increasingly precise discipline with the advent of high-luminosity experiments at both colliders and fixed-target facilities
To assess information about the PDFs encapsulated in the residuals for large collections of hadronic data implemented in the CTEQTEA global analysis, we make available a new statistical package PDFSENSE to map the regions of partonic momentum fractions x and QCD factorization scales μ where the experiments impose strong constraints on the PDFs
In the comparisons we made, the detailed pictures produced by both PDFSENSE and the Lagrange multiplier (LM) scans depend on a variety of theoretical settings like perturbative QCD (pQCD) scale choices, as well as upon the specific implementation of correlated experimental uncertainties and the parametric forms chosen for the nonperturbative parametrizations at the starting scale μ 1⁄4 Q0
Summary
The determination of collinear parton distribution functions (PDFs) of the nucleon is becoming an increasingly precise discipline with the advent of high-luminosity experiments at both colliders and fixed-target facilities. To assess information about the PDFs encapsulated in the residuals for large collections of hadronic data implemented in the CTEQTEA global analysis, we make available a new statistical package PDFSENSE to map the regions of partonic momentum fractions x and QCD factorization scales μ where the experiments impose strong constraints on the PDFs. In companion studies, we have applied PDFSENSE to select new data sets for the generation of the CTEQ-TEA global analysis, to quantitatively explore the physics potential for constraining the PDFs at a future ElectronIon Collider [65,66,67,68] and Large Hadron-Electron Collider [69], and to investigate the potential of high-energy data to inform lattice-calculable quantities [70] like the Mellin moments of structure functions [71] and quark quasidistributions [72]. Additional aspects of the technique and supplementary tables are reserved for Appendixes A and B, respectively
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